@article{700cca99deab446b9283e93f4b27375b,
title = "A sauer–shelah–perles lemma for lattices",
abstract = "We study lattice-theoretical extensions of the celebrated Sauer–Shelah–Perles Lemma. We conjecture that a general Sauer–Shelah–Perles Lemma holds for a lattice if and only if the lattice is relatively complemented, and prove partial results towards this conjecture.",
author = "Stijn Cambie and Bogdan Chornomaz and Zeev Dvir and Yuval Filmus and Shay Moran",
note = "Funding Information: ∗Research supported by a Vidi Grant of the Netherlands Organization for Scientific Research (NWO), grant number 639.032.614. †Research supported by NSF CAREER award DMS-1451191 and NSF grant CCF-1523816. Work on this paper was done while the author was a Von-Neumann fellow at the Institute for Advanced Study, supported by a Simons foundation fellowship. ‡Taub Fellow — supported by the Taub Foundations. The research was funded by ISF grant 1337/16. §Research supported by the Israel Science Foundation (grant No. 1225/20), by an Azrieli Faculty Fellowship, and by a grant from the United States — Israel Binational Science Foundation (BSF). Publisher Copyright: {\textcopyright} The authors.",
year = "2020",
doi = "10.37236/9273",
language = "English (US)",
volume = "27",
pages = "1--21",
journal = "Electronic Journal of Combinatorics",
issn = "1077-8926",
publisher = "Electronic Journal of Combinatorics",
number = "4",
}